A magnetized plasma radial fluid model calculation method based on inverse mapping physical information neural network

Abstract

The application discloses a kind of magnetized plasma radial fluid model calculation method based on inverse mapping physical information neural network, it is related to plasma physics simulation and computational fluid dynamics cross field.This application breaks the limitation of specific plasma source type, for covering space electric thruster, semiconductor etching and deposition equipment and other extensive magnetized plasma industrial device, provide a kind of high-precision, strong robustness and easy to operate internal flow field fast prediction and parameter optimization tool.Meanwhile, by introducing logarithmic parameterization and dynamic decoding mechanism, the extended architecture of the application also has fully end-to-end physical parameter automatic discovery capability, completely solves the network gradient imbalance problem caused by extreme span physical quantity, makes the algorithm completely get rid of the dependence on external numerical prior solution, has revolutionary application potential in non-invasive diagnosis and digital twin field.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of plasma physics simulation and computational fluid dynamics, specifically to a method for calculating a radial fluid model of plasma that is widely used in various magnetized plasma devices, and a method for autonomous identification of plasma characteristic parameters based on logarithmic parameterization. Background Technology

[0002] To delve into the discharge maintenance mechanism and multiphysics coupling effects of the aforementioned magnetized plasma devices under complex magnetic field confinement, researchers typically employ one-dimensional (1D) radial fluid models to elucidate core physical processes such as bipolar diffusion, sheath structure, and wall loss mechanisms. Regarding the numerical solution of this model, existing traditional literature and conventional computational fluid dynamics schemes usually rely on the shooting method or the finite-difference time-domain (FDTD) method. In the shooting method, iterative solutions are made by continuously adjusting initial guesses to solve multi-point boundary value problems; while in the FDTD method, differential equations are discretized and the physical fields are solved by spatially dividing the computational grid. Furthermore, recent publications on low-temperature plasma simulations have also revealed a solution method using standard physical information neural networks (PINNs). In this standard PINN method, radial spatial coordinates are typically directly... As an independent input variable of the neural network, it directly outputs the corresponding plasma physical field (such as electron density, radial velocity, etc.) through the forward propagation of the network.

[0003] In both traditional numerical methods, the plasma transport equations exhibit highly nonlinear multiphysics coupling characteristics. Particularly with increasing applied magnetic field strength and drastic changes in source terms (ionization, collisions), the fluid equations demonstrate extremely significant stiffness. This stiffness makes the target method highly sensitive to initial guesses, easily getting trapped in local optima or leading to computational divergence. On the other hand, when analyzing high-gradient regions with drastically changing parameters, such as the plasma sheath near the wall, the finite difference method exhibits strong mesh dependence, requiring extremely complex non-uniform meshes to barely guarantee computational accuracy.

[0004] Furthermore, in the solution scheme of the aforementioned standard Physical Information Neural Networks (PINNs), spatial coordinates are directly used. Mapping to physical fields also faces serious technical drawbacks. First, the rigidity of equations under strong magnetic field conditions easily leads to gradient explosion or vanishing during backpropagation in neural networks, causing training failure. More critically, due to the inherent properties of cylindrical coordinates, the fluid equations exhibit a certain degree of rigidity near the horizontal axis. Proportional geometric singularities; in the standard input frame, when spatial coordinates When approaching zero, directly calculating these singular terms inevitably leads to division-by-zero errors and numerical divergence. Therefore, constrained by the triple challenges of equation rigidity caused by strong magnetic fields, high gradients in the sheath, and axial geometric singularities, existing techniques struggle to reconstruct the complex plasma distribution across the entire radial domain with stable and high precision.

[0005] On the other hand, when faced with unknown discharge conditions, plasma fluid models often have globally unknown core parameters (such as the central characteristic density at discharge equilibrium). This parameter often has an extremely high order of magnitude (e.g., Directly optimizing these extreme parameters in conventional physical information neural networks can lead to severe parameter stiffness and gradient imbalance. Over-reliance on pre-solving through target acquisition undermines the end-to-end automation of deep learning, limiting its diagnostic potential in the field of digital twins. Summary of the Invention

[0006] The technical problem this invention aims to solve is to overcome the shortcomings of existing technologies that use traditional numerical methods and standard physical information neural networks to solve radial fluid models of magnetized plasmas. Specifically, it addresses the rigidity of equations caused by strong magnetic field constraints and multi-field coupling, the geometric singularity at the axis of the computational domain (i.e., division-by-zero divergence), and the difficulty in accurately analyzing high-gradient regions of the sheath. This invention provides a solution method based on inverse mapping physical information neural networks (IM-PINN), which can efficiently, stably, and accurately reconstruct the complex spatial distribution characteristics of magnetized plasma physical quantities.

[0007] This invention provides a method for calculating a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network. The method includes:

[0008] Step 1: Construct the fluid equations and physical boundary conditions describing the radial transport process of magnetized plasma;

[0009] The ion sound velocity and plasma radius are treated as dimensionless features to establish a four-equation fluid model that includes mass conservation, radial momentum conservation, angular momentum conservation, and potential equations.

[0010] (1);

[0011] (2);

[0012] (3);

[0013] (4);

[0014] in,, To achieve dimensionless low clutter frequencies, This represents the effective collision frequency related to axial diffusion. The dimensionless ion collision frequency. The dimensionless ionization frequency, The dimensionless electron collision frequency, For electronic quality, It refers to the ion mass;

[0015] The boundary conditions are: at the axis center, i.e., radial spatial coordinates At that point, scalar field density and electric potential Satisfies even symmetry, i.e., the derivative is zero; radial velocity of the vector field. Angular velocity It satisfies odd symmetry, i.e., the value is zero; at the edge of the sheath, i.e., radial spatial coordinates At this point, the velocity of the ionic fluid must satisfy the Bohm criterion;

[0016] Step 2: Construct a fully connected feedforward neural network, utilizing the electron radial velocity The monotonically increasing physical property will affect the radial velocity. As the sole independent input variable of the neural network;

[0017] Step 3: Reconstruct and output the corresponding radial space coordinates through the output layer of the neural network. ,density Electron angular velocity and bipolar potential .

[0018] Furthermore, the specific method for the fully connected feedforward neural network in step 2 is as follows:

[0019] Normalized ion radial velocity As the core spatially independent input variable, the computational domain is defined in velocity space. Inside, the output layer variables of the fully connected feedforward neural network are radial spatial coordinates. And the plasma state vector includes: density Angular velocity and electric potential This fully connected feedforward neural network contains six hidden layers, each with 256 neurons. All hidden layers use hyperbolic tangent as the activation function, and the network weights are initialized using the Xavier scheme. During network training, a total loss function is constructed. as follows:

[0020] (5);

[0021] (6);

[0022] (7);

[0023] In the formula: For the physical residual loss of partial differential equations, The loss is due to boundary condition constraints, specifically the loss from the axisymmetric boundary. and sheath boundary loss composition; and These are the weighting coefficients for physical residual loss and boundary condition loss, respectively. This represents the total number of configuration points sampled within the computational domain; Indicates the first The first configuration point The transformation residuals of the partial differential equations .

[0024] Furthermore, in the computational fluid dynamics equations regarding the radial coordinates... The method for finding the spatial derivative is as follows:

[0025] When constructing the physical information loss function, the chain rule is used to... The differential operator is transformed into a function of the input variable. The derivative, i.e., the inverse Jacobian term, is introduced. To calculate the residuals of the partial differential equations; using the above method, specifically construct the transformation residuals of four partial differential equations. as follows:

[0026] (8);

[0027] (9);

[0028] (10);

[0029] (11);

[0030] In the formula: For the inverse Jacobian term; $ , These are the output variables of the neural network in relation to the input variables. The gradient is obtained through automatic differentiation; the meanings of the remaining physical symbols remain consistent with those in the original fluid equations.

[0031] Furthermore, for the geometrically singular terms present at the axis in the fluid equations, at the input node of the neural network... At this point, the limit of the singular term is explicitly replaced with the inverse Jacobian term. .

[0032] Furthermore, for unknown feature centers and feature densities An end-to-end autonomous identification strategy is provided, namely, constructing a log-parameterized path and using the central feature density. Mapped to dimensionless trainable parameters on a logarithmic scale Its mapping formula is ,in For characteristic frequencies, This is a prefactor of the electron-ion collision constant; in network forward propagation, through a dynamic decoding mechanism, the formula is used... Will The central feature density is reduced to a physical quantity and substituted into the residuals of the four partial differential equations constructed above, i.e., equations (8), (9), (10), and (11), to calculate the total loss function; during backpropagation, a coupled optimization strategy is executed to calculate and update the spatial distribution weights. With dimensionless trainable parameters : Calculate the total loss function using automatic differentiation techniques and The gradient is calculated using the Adam optimizer for gradient descent; during the update process, an asymmetric gradient pruning strategy is applied to the spatially distributed weights. The gradient maximum norm is clipped to 1.0 to prevent spatial profile oscillations, and the feature parameters are... The maximum norm of the gradient is relaxed to 10.0 to allow for rapid exploration through synchronous iterative updates. and The network continues until it converges, at which point it autonomously outputs the precise value of the unknown physical parameter.

[0033] Furthermore, a hybrid solution strategy was adopted, which involves pre-determining the central characteristic density at discharge equilibrium using the traditional numerical target shooting method. The physical constraint parameter is embedded into the loss function of the neural network, so that the neural network focuses on analyzing the spatial distribution of high gradients. The neural network uses hyperbolic tangent as the activation function to ensure the high-order differentiability required by the equation, and uses the Adam optimizer to minimize the loss function iteratively.

[0034] Compared to existing technologies, the technical solution employed in this invention delivers a significant leap in computational performance and engineering application value. Firstly, this invention innovatively employs an inverse mapping neural network architecture, which transforms radial velocity... As an independent input variable, and combined with asymptotic analysis constraints, the mathematical mechanism eliminates the limitations of traditional cylindrical coordinate fluid models at the axis. The problem of division-to-zero divergence caused by singular terms. This core improvement not only ensures that the plasma state variables maintain strict physical parity symmetry and extremely high numerical smoothness at the axis, but also fundamentally improves the computational accuracy and numerical stability of multiphysics coupled simulations. Secondly, in traditional numerical simulations, in order to accurately analyze the sheath region where plasma physical quantities change drastically, it is usually necessary to rely on manual experience to design extremely complex non-uniform spatial grids; while this invention introduces inverse Jacobian terms. Converting the spatial derivative to the velocity derivative fully leverages the meshless advantage of physical information neural networks. This method, because it converts the spatial derivative to the velocity derivative, fully utilizes the meshless advantage of physical information neural networks. The invention employs uniform point sampling, an inverse mapping mechanism that allows the network to naturally allocate more physical space sampling weights at the sheath edge where physical gradients are extremely large and velocities change rapidly. This implicitly achieves adaptive mesh refinement, greatly simplifying the pre-processing steps while accurately capturing the steep spatial structure of the sheath region. Finally, for complex fluid systems involving multi-physics coupling such as density, velocity, and potential, the solution framework effectively overcomes the extremely rigid characteristics of partial differential equations under strong magnetic field conditions, avoiding the shortcomings of traditional target-shooting methods that easily fall into local optima or divergence when dealing with multi-point boundary value problems. Verification shows that, regardless of whether under weak magnetic confinement or extremely rigid strong magnetic confinement, the invention maintains extremely high robustness and stable convergence, accurately reconstructing the potential drop and density decay curves. This invention breaks the limitations of specific plasma source types, providing a high-precision, robust, and easy-to-operate tool for rapid prediction and parameter optimization of internal flow fields for a wide range of magnetized plasma industrial devices, including space electric thrusters and semiconductor etching and deposition equipment. Furthermore, by introducing logarithmic parameterization and dynamic decoding mechanisms, the extended architecture of this invention also possesses a fully end-to-end automatic physical parameter discovery capability, completely solving the problem of extreme span physical quantities (such as...) The network gradient imbalance problem caused by the density of the network (of magnitude) has enabled the algorithm to completely get rid of its dependence on external numerical prior solutions, and has disruptive application potential in the fields of non-invasive diagnosis and digital twins. Attached Figure Description

[0035] Figure 1 This is a flowchart of the magnetized plasma solution method based on the inverse mapping physical information neural network according to the present invention;

[0036] Figure 2 This is a schematic diagram of the geometric structure of the cylindrical magnetized plasma source according to the present invention;

[0037] Figure 3 This is a schematic diagram of the forward and backward propagation computational architecture of the Inverse Mapping Physical Information Neural Network (IM-PINN) according to the present invention;

[0038] Figure 4 This is a comparison graph of the radial velocity, logarithmic density, and bipolar potential output by an embodiment of the present invention under a weak magnetic field (150G) condition in a local equilibrium fluid model, with the reference numerical solution.

[0039] Figure 5 This is a comparison graph of the radial velocity, logarithmic density, and bipolar potential output by an embodiment of the present invention under a strong magnetic field (600G) condition in a local equilibrium fluid model, with the reference numerical solution.

[0040] Figure 6 This is a comparison chart of the radial velocity, logarithmic density, bipolar potential, and angular velocity output by an embodiment of the present invention under a weak magnetic field (150G) condition in a fully coupled fluid model, with the reference numerical solution.

[0041] Figure 7 This is a comparison chart of the radial velocity, logarithmic density, bipolar potential, and angular velocity output by an embodiment of the present invention under a strong magnetic field (600G) in a fully coupled fluid model, with the reference numerical solution.

[0042] Figure 8 This is a curve showing the convergence evolution of the characteristic density parameters autonomously identified by the network under a weak magnetic field (150G) working condition in a local equilibrium fluid model according to the present invention.

[0043] Figure 9 This is a curve showing the convergence evolution of the characteristic density parameters autonomously identified by the network under a strong magnetic field (600G) working condition in a local equilibrium fluid model according to the present invention.

[0044] Figure 10 This is a curve showing the convergence evolution of the characteristic density parameters autonomously identified by the network under a weak magnetic field (150G) in a fully coupled fluid model.

[0045] Figure 11 This is a curve showing the convergence evolution of the characteristic density parameters autonomously identified by the network under a strong magnetic field (600G) in a fully coupled fluid model according to the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0047] like Figure 1 As shown, this invention provides a method for solving magnetized plasma based on an inverse mapping physical information neural network. The method specifically includes the following steps:

[0048] Step S101: Obtain the dimensionless radial fluid equations and physical boundary conditions of the magnetized plasma.

[0049] For example Figure 2 The geometry of the cylindrical magnetized plasma source is shown. A four-equation fluid model is established, incorporating mass conservation, radial momentum conservation, angular momentum conservation, and potential equations. Ion sound velocity and plasma radius are treated as dimensionless characteristic scales. In this model, the boundary conditions are defined as follows: at the axis ( At that location, the scalar field (density) electric potential It satisfies even symmetry, i.e., the derivative is zero; vector field (radial velocity) Angular velocity ) satisfies odd symmetry, that is, the value is zero. At the edge of the sheath ( At point ), the ionic fluid velocity must satisfy the Bohm criterion, i.e. .

[0050] Step S102: Construct the Inverse Mapping Physical Information Neural Network (IM-PINN).

[0051] like Figure 3 As shown, unlike the traditional PINN framework, this invention constructs a fully connected feedforward neural network to normalize the ion radial velocity. As a core spatially independent input variable (when the autonomous recognition strategy is enabled, the network also includes logarithmic feature parameters), (Input and decoding paths), the computational domain is defined in velocity space. The network's output layer variables are radial spatial coordinates. and plasma state vector (including density) Angular velocity and electric potential In this embodiment, the neural network contains 6 hidden layers, each with 256 neurons. To ensure the high-order differentiability required by the fluid equations, all hidden layers use hyperbolic tangent (tanh) as the activation function, and the network weights are initialized using the Xavier scheme.

[0052] Step S103: Construct the residuals of the partial differential equation using the chain rule.

[0053] Because the original radial fluid equations contain information about spatial coordinates... The derivative of the network output of this invention. It's already about The function is such that the space transformation of the differential operator is performed using the chain rule. For any state variable... The spatial derivative is calculated as follows:

[0054] (12);

[0055] The above formula introduces an inverse Jacobian term into the calculation of PDE residuals. This allows for the precise calculation of the transformation residuals of the continuity equation, momentum equation, and potential equation using an automatic differential engine.

[0056] Step S104: Eliminate geometric singularities by combining asymptotic analysis.

[0057] The fluid equations contain, for example, The cylindrical coordinate geometric singularity, when the input variable At that time, the radius of the network output It also approaches zero, and direct calculation will lead to division by zero divergence. Therefore, the pivot point of the network (i.e., the input) is located at the axis of the network. At point ), based on Taylor expansion and L'Hôpital's rule, this invention explicitly replaces the limit of the divergence term with its derivative value:

[0058] (13);

[0059] In conjunction with the inverse Jacobian term from step S103, the following replacement is performed in the computation graph:

[0060] (14);

[0061] This completely eliminates geometric singularities from the computational graph.

[0062] Step S105: Global feature parameter processing and loss function construction.

[0063] For the central characteristic density at discharge equilibrium in the physical model This invention provides two parallel processing strategies:

[0064] Strategy 1 (Hybrid Solution Strategy): Pre-calculate the feature density using the target shooting method. And it is embedded in the model as a fixed physical constraint.

[0065] Strategy Two (Autonomous Identification Strategy): In order to achieve inversion without any external intervention, Convert to dimensionless parameters And define scalar trainable parameters in the neural network. During network forward propagation, a dynamic decoding formula is used. The exploration The experimental characteristic density is restored and used in the loss calculation.

[0066] Step S106: Iterative optimization.

[0067] The Adam optimizer is employed. For strategy one, only the weights within the network are optimized; for strategy two, a coupled optimization strategy is implemented, synchronously iteratively updating the network weights during backpropagation. With logarithmic characteristic parameters The process continues until the total loss function converges, outputting the spatial distribution of plasma physical quantities (as well as the results of autonomously identified core feature parameters).

[0068] To verify the broad adaptability and robustness of the method of the present invention under different physical conditions, four specific simulation examples are provided below:

[0069] Example 1 (Local Equilibrium Fluid Model Working Condition): Under this working condition, the electronic inertia term is ignored based on the local equilibrium assumption to simplify the model. As shown in Figures 4 and 5, under weak magnetic fields (150G) and strong magnetic fields (600G), the radial velocity, electron density, and potential distribution curves predicted by the method of this invention highly coincide with the traditional high-precision numerical solutions.

[0070] Example 2 (Fully Coupled Fluid Model Condition): In this condition, a complete electron angular momentum differential equation is introduced, considering electron inertia and nonlocal transport effects, further enhancing the rigidity of the equation. As shown in Figures 6 and 7, facing more drastic wall gradient changes, the inverse mapping network of this invention can not only accurately reconstruct density and potential, but also successfully capture the drastic nonlinear changes in electron angular velocity in the sheath region without generating any spurious oscillations.

[0071] Example 3 (Autonomous identification of 150G operating parameters under a local equilibrium fluid model): For example... Figure 8 As shown, under the local equilibrium fluid model, the logarithmic parameterization path makes the trainable parameters... After rapid adjustments, the network finally autonomously locked the feature density parameters with a very small relative error of only 0.012% compared to the true values, successfully achieving a fully end-to-end high-precision parameter inversion.

[0072] Example 4 (Autonomous identification of 600G operating parameters under a local equilibrium fluid model): For example... Figure 9 As shown, with the increase of the magnetic field, the coupling optimization architecture of the present invention still exhibits strong robustness under the local equilibrium model, and the final relative recognition error is only -0.027%.

[0073] Example 5 (Autonomous Parameter Identification for 150G Operating Conditions under a Fully Coupled Fluid Model): In the fully coupled fluid model considering electronic inertia, the rigidity of the equations is further enhanced. For example... Figure 10 As shown, the method of the present invention exhibits extremely high inversion accuracy under this complex working condition, with the final relative identification error reaching an astonishing 0.000%.

[0074] Example 6 (Autonomous identification of parameters under a 600G strong magnetic field in a fully coupled fluid model): For example... Figure 11 As shown, even under the most severe fully coupled strong magnetic field conditions, the network can still converge stably, and the relative error between the feature density parameters that are finally autonomously identified and the true values ​​is only 0.001%.

[0075] The above six complete embodiments, covering extreme magnetic field conditions at both ends and different equation complexities, fully demonstrate that the present invention is not limited to specific plasma parameters and simplified models. For any complex fluid problem with cylindrical symmetry, it can achieve high-precision robust simulation without complex meshes and has an extremely powerful and accurate parameter autonomous discovery capability.

Claims

1. A calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network, the method comprising: Step 1: Construct the fluid equations and physical boundary conditions describing the radial transport process of magnetized plasma; The ion sound velocity and plasma radius are treated as dimensionless features to establish a four-equation fluid model that includes mass conservation, radial momentum conservation, angular momentum conservation, and potential equations. （1）； （2）； （3）； （4）； in, To achieve dimensionless low clutter frequencies, This represents the effective collision frequency related to axial diffusion. The dimensionless ion collision frequency. The dimensionless ionization frequency, The dimensionless electron collision frequency, For electronic quality, It refers to the ion mass; The boundary conditions are: at the axis center, i.e., radial spatial coordinates At that point, scalar field density and electric potential Satisfies even symmetry, i.e., the derivative is zero; radial velocity of the vector field. Angular velocity It satisfies odd symmetry, i.e., the value is zero; at the edge of the sheath, i.e., radial spatial coordinates At this point, the velocity of the ionic fluid must satisfy the Bohm criterion; Step 2: Construct a fully connected feedforward neural network, utilizing the electron radial velocity The monotonically increasing physical property will affect the radial velocity. As the sole independent input variable of the neural network; Step 3: Reconstruct and output the corresponding radial space coordinates through the output layer of the neural network. ,density Electron angular velocity and bipolar potential .

2. The calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network as described in claim 1, characterized in that, The specific method for the fully connected feedforward neural network in step 2 is as follows: Normalized ion radial velocity As the core spatially independent input variable, the computational domain is defined in velocity space. Inside, the output layer variables of the fully connected feedforward neural network are radial spatial coordinates. And the plasma state vector includes: density Angular velocity and electric potential This fully connected feedforward neural network contains six hidden layers, each with 256 neurons. All hidden layers use hyperbolic tangent as the activation function, and the network weights are initialized using the Xavier scheme. During network training, a total loss function is constructed. as follows: （5）； （6）； （7）； In the formula: For the physical residual loss of partial differential equations, The loss is due to boundary condition constraints, specifically the loss from the axisymmetric boundary. and sheath boundary loss composition; and These are the weighting coefficients for physical residual loss and boundary condition loss, respectively. This represents the total number of configuration points sampled within the computational domain; Indicates the first The first configuration point The transformation residuals of the partial differential equations .

3. The calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network as described in claim 1, characterized in that, The computational fluid dynamics equations regarding radial coordinates The method for finding the spatial derivative is as follows: When constructing the physical information loss function, the chain rule is used to... The differential operator is transformed into a function of the input variable. The derivative, i.e., the introduction of the inverse Jacobian term. To calculate the residuals of the partial differential equations; using the above method, specifically construct the transformation residuals of four partial differential equations. as follows: （8）； （9）； （10）； （11）； In the formula: For the inverse Jacobian term; $ , These are the output variables of the neural network in relation to the input variables. The gradient is obtained through automatic differentiation; the meanings of the remaining physical symbols remain consistent with those in the original fluid equations.

4. The calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network as described in claim 1, characterized in that, For the geometrically singular terms present at the axis in the fluid equations, at the input node of the neural network... At this point, the limit of the singular term is explicitly replaced with the inverse Jacobian term. .

5. The calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network as described in claim 2, characterized in that, For unknown feature centers and feature density An end-to-end autonomous identification strategy is provided, namely, constructing a log-parameterized path and using the central feature density. Mapped to dimensionless trainable parameters on a logarithmic scale Its mapping formula is ,in For characteristic frequencies, This is a prefactor of the electron-ion collision constant; in network forward propagation, through a dynamic decoding mechanism, the formula is used... Will The central feature density is reduced to a physical quantity and substituted into the residuals of the four partial differential equations constructed above, i.e., equations (8), (9), (10), and (11), to calculate the total loss function; during backpropagation, a coupled optimization strategy is executed to calculate and update the spatial distribution weights. With dimensionless trainable parameters : Calculate the total loss function using automatic differentiation techniques and The gradient is calculated using the Adam optimizer for gradient descent; during the update process, an asymmetric gradient pruning strategy is applied to the spatially distributed weights. The gradient maximum norm is clipped to 1.0 to prevent spatial profile oscillations, and the feature parameters are... The maximum norm of the gradient is relaxed to 10.0 to allow for rapid exploration through synchronous iterative updates. and The network continues until it converges, at which point it autonomously outputs the precise value of the unknown physical parameter.

6. The calculation method for a radial fluid model of magnetized plasma based on an inverse mapping physical information neural network as described in claim 2, characterized in that, A hybrid solution strategy was also adopted, which involved pre-determining the central characteristic density at discharge equilibrium using the traditional numerical target shooting method. The physical constraint parameter is embedded into the loss function of the neural network, so that the neural network focuses on analyzing the spatial distribution of high gradients. The neural network uses hyperbolic tangent as the activation function to ensure the high-order differentiability required by the equation, and uses the Adam optimizer to minimize the loss function iteratively.

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